It's a little ... annoying.
It happens to both my ATI card and Nvidia card running proprietary drivers.
This hasn't always happened. Version 1.0 of Wine for example doesn't exhibit this behaviour.
The workaround is a little clunky; before running the game, use xrandr to check the available modes and then use xrandr to set the game resolution
e.g. launching a terminal and running xrandr:
chocobo:~$ xrandr
Screen 0: minimum 8 x 8, current 1920 x 1080, maximum 16384 x 16384
DVI-I-0 disconnected (normal left inverted right x axis y axis)
VGA-0 disconnected (normal left inverted right x axis y axis)
DVI-I-1 connected primary 1920x1080+0+0 (normal left inverted right x axis y axis) 477mm x 268mm
1920x1080 60.0*+
1680x1050 60.0
1280x1024 75.0 60.0
1152x864 75.0
1024x768 75.0 60.0
800x600 75.0 60.3
640x480 75.0 59.9
HDMI-0 disconnected (normal left inverted right x axis y axis)
xrandr --output DVI-I-1 --mode 1024x768
The desktop will resize to this resolution.
Start your Wine game. It should fit the viewport on your monitor.
Once you exit, set the resolution back to the default desktop setting:
xrandr --output DVI-I-1 --mode 1920x1080